Problem: Solve for $x$ and $y$ using elimination. ${-3x+y = -12}$ ${4x-4y = 8}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ ${-12x+4y = -48}$ $4x-4y = 8$ Add the top and bottom equations together. $-8x = -40$ $\dfrac{-8x}{{-8}} = \dfrac{-40}{{-8}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-3x+y = -12}\thinspace$ to find $y$ ${-3}{(5)}{ + y = -12}$ $-15+y = -12$ $-15{+15} + y = -12{+15}$ ${y = 3}$ You can also plug ${x = 5}$ into $\thinspace {4x-4y = 8}\thinspace$ and get the same answer for $y$ : ${4}{(5)}{ - 4y = 8}$ ${y = 3}$